http://www.colloquiam.com/wd/index.php?action=history&feed=atom&title=Berzins_2023b Berzins 2023b - Revision history 2026-05-11T18:21:23Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 http://www.colloquiam.com/wd/index.php?title=Berzins_2023b&diff=288412&oldid=prev JSanchez: JSanchez moved page Draft Sanchez Pinedo 514135632 to Berzins 2023b 2023-11-23T15:00:44Z <p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_514135632" class="mw-redirect" title="Draft Sanchez Pinedo 514135632">Draft Sanchez Pinedo 514135632</a> to <a href="/public/Berzins_2023b" title="Berzins 2023b">Berzins 2023b</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <tr style='vertical-align: top;' lang='en'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 15:00, 23 November 2023</td> </tr><tr><td colspan='2' style='text-align: center;' lang='en'><div class="mw-diff-empty">(No difference)</div> </td></tr></table> JSanchez http://www.colloquiam.com/wd/index.php?title=Berzins_2023b&diff=288411&oldid=prev JSanchez at 15:00, 23 November 2023 2023-11-23T15:00:40Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:00, 23 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The Material Point Method (MPM) is widely used for challenging applications in engineering, and animation but lags behind some other methods in terms of error analysis and computable error estimates. The complexity and nonlinearity of the equations solved by the method and its reliance both on a mesh and on moving particles makes error estimation challenging. Some preliminary error analysis of a simple MPM method has shown the global error to be first order in space and time for a widely-used variant of the Material Point Method. The overall time dependent nature of MPM also complicates matters as both space and time errors and their evolution must be considered thus leading to the use of explicit error transport equations. The preliminary use of an error estimator based on this transport approach has yielded promising results in the 1D case. One other source of error in MPM is the grid-crossing error that can be problematic for large deformations leading to large errors that are identified by the error estimator used. The extension of the error estimation approach to two space higher dimensions is considered and together with additional algorithmic and theoretical results, shown to give promising results in preliminary computational experiments.</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The Material Point Method (MPM) is widely used for challenging applications in engineering, and animation but lags behind some other methods in terms of error analysis and computable error estimates. The complexity and nonlinearity of the equations solved by the method and its reliance both on a mesh and on moving particles makes error estimation challenging. Some preliminary error analysis of a simple MPM method has shown the global error to be first order in space and time for a widely-used variant of the Material Point Method. The overall time dependent nature of MPM also complicates matters as both space and time errors and their evolution must be considered thus leading to the use of explicit error transport equations. The preliminary use of an error estimator based on this transport approach has yielded promising results in the 1D case. One other source of error in MPM is the grid-crossing error that can be problematic for large deformations leading to large errors that are identified by the error estimator used. The extension of the error estimation approach to two space higher dimensions is considered and together with additional algorithmic and theoretical results, shown to give promising results in preliminary computational experiments.</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Full Paper ==</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&lt;pdf&gt;Media:Draft_Sanchez Pinedo_514135632pap_29.pdf&lt;/pdf&gt;</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:288409:newid:288411 --> </table> JSanchez http://www.colloquiam.com/wd/index.php?title=Berzins_2023b&diff=288409&oldid=prev JSanchez at 15:00, 23 November 2023 2023-11-23T15:00:37Z <p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 15:00, 23 November 2023</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">&#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; &#160; </ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Abstract==</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The Material Point Method (MPM) is widely used for challenging applications in engineering, and animation but lags behind some other methods in terms of error analysis and computable error estimates. The complexity and nonlinearity of the equations solved by the method and its reliance both on a mesh and on moving particles makes error estimation challenging. Some preliminary error analysis of a simple MPM method has shown the global error to be first order in space and time for a widely-used variant of the Material Point Method. The overall time dependent nature of MPM also complicates matters as both space and time errors and their evolution must be considered thus leading to the use of explicit error transport equations. The preliminary use of an error estimator based on this transport approach has yielded promising results in the 1D case. One other source of error in MPM is the grid-crossing error that can be problematic for large deformations leading to large errors that are identified by the error estimator used. The extension of the error estimation approach to two space higher dimensions is considered and together with additional algorithmic and theoretical results, shown to give promising results in preliminary computational experiments.</ins></div></td></tr> <!-- diff cache key mw_drafts_scipedia-sc_mwd_:diff:version:1.11a:oldid:288408:newid:288409 --> </table> JSanchez http://www.colloquiam.com/wd/index.php?title=Berzins_2023b&diff=288408&oldid=prev JSanchez: Created blank page 2023-11-23T15:00:34Z <p>Created blank page</p> <p><b>New page</b></p><div></div> JSanchez